It would not change the tax-inclusive cost of housing. Land taxes can not be passed on.
You are right, that the tax-inclusive cost of housing won't change with a land tax on its own, at least not as a first order effect.
If however, you eg use the land tax proceeds to lower taxes on labour and capital, building higher (ie using more capital for housing) will become more economically feasible. (No economic revenue will be lost. Lower taxes in a jurisdiction directly lead to higher land prices---which the land tax will capture.)
You are right, that the tax-inclusive cost of housing won't change with a land tax on its own, at least not as a first order effect.
If however, you eg use the land tax proceeds to lower taxes on labour and capital, building higher (ie using more capital for housing) will become more economically feasible. (No economic revenue will be lost. Lower taxes in a jurisdiction directly lead to higher land prices---which the land tax will capture.)
There's also some other second order effects, like less NIMBYism. (https://www.dartmouth.edu/~wfischel/Papers/00-04.PDF) This will make development easier.